Help Mathematical Statistics questions in matematica !!!</SPAN></SPAN>

Win a teddy bear at a dice game throws you five dice in the form of the Platonic bodies. The dice are numbered with the integers 1,2, ..., n where n is the number of pages. After throwing it summarizes the numbers on the pages are upturned, but the tetrahedron is the century (1-4) written in the tip pointing upwards.

1. Your first task is to accurately determine the probability function for the sum S and state E (S) and D (S).

At a carnival is a position where you can win a big teddy bear if you participate in the mentioned dice game. You invest €3, and then throw the five dice. If the total meets the conditions (S £ 10+S ³ 45) you win the teddy bear. The carnival valued the teddy bear at € 100 (but purchased for € 60).

2. Determine the exact probability of teddy profit and determine also the average profit that the Carnival makes per one player.

Solution:

To obtain the sum of the probability of throwing five Platonic dice. I use Tuples to generate a list of possible n - Tuple of elements from the list. All possible 5 - Tuples of (1 , 4), (1, 6), (1, 8), (1, 12), (1, 20)</SPAN></SPAN>

W=Tuples[{ Range[1,4],Range[1, 6],Range[1,8],Range[1,12],Range[1,20]}]

Short[W]

I did the first question but not the second somewere I lost to determine the average profit that the Carnival makes per one player.